Coherent States for Transparent Potentials

Abstract

Darboux transformation operators that produce multisoliton potentials are analyzed as operators acting in a Hilbert space. Isometric correspondence between Hilbert spaces of states of a free particle and a particle moving in a soliton potential is established. It is shown that the Darboux transformation operator is unbounded but closed and can not realize an isometric mapping between Hilbert spaces. A quasispectral representation of such an operator in terms of continuum bases is obtained. Different types of coherent states of a multisoliton potential are introduced. Measures that realize the resolution of the identity operator in terms of the projectors on the coherent states vectors are calculated. It is shown that when these states are related with free particle coherent states by a bounded symmetry operator the measure is defined by ordinary functions and in the case of a semibounded symmetry operator the measure is defined by a generalized function.

References in corpus (3)

• A General Theory of Phase-Space Quasiprobability Distributions
• Non-linear coherent states associated with conditionally exactly solvable problems
• Supersymmetry and Supercoherent States of a Nonrelativistic Free Particle

Cited by in corpus (7)

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• SUSY transformations with complex factorization constants. Application to spectral singularities
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• Darboux transformations of coherent states of the time-dependent singular oscillator
• Transparent lattices and their solitary waves
• Supersymmetry approach to nuclear-spin-polarization-induced quantum dot structure calculations